Abstract

A new, to our knowledge, method for evaluating three-dimensional flux distributions for general filament light sources is presented. The main advantages of the developed model are its generality and its simplicity. From plots of the emitted luminous intensity, usually provided by the lamp’s manufacturer, in three orthogonal planes a detailed account is given of how to establish flux emission from the light source in any direction. The method involves a selective smoothing procedure, a curve-fitting step, and a final interpolation. A full model is developed for a typical commercial filament bulb (Philips, Model P21W Inco K) that is quite common in many industrial applications. A fourth intensity plot, usually provided by the lamp’s manufacturer, is used to validate the model. To confirm the validity of the model further, we present an industrial application (the photometric simulation of a car taillight) that uses the modeled Philips Model P21W source. A comparison between simulated data obtained by use of the developed P21W model and measured results at our industrial partner’s laboratories reinforces the proposed source model.

© 1999 Optical Society of America

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References

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  1. R. Winston, H. Ries, “Nonimaging reflectors as functionals of the desired irradiance,” J. Opt. Soc. Am. A 10, 1902–1908 (1993).
    [CrossRef]
  2. J. C. Miñano, J. C. González, “New method of design for nonimaging concentrators,” Appl. Opt. 31, 3051–3060 (1992).
    [CrossRef] [PubMed]
  3. I. Powell, A. Brewsher, “Software development for design of illumination systems,” Opt. Eng. 33, 1678–1683 (1994).
    [CrossRef]

1994 (1)

I. Powell, A. Brewsher, “Software development for design of illumination systems,” Opt. Eng. 33, 1678–1683 (1994).
[CrossRef]

1993 (1)

1992 (1)

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Figures (10)

Fig. 1
Fig. 1

Reference system described in the text. The X axis runs from the metallic base of the bulb to its glass top; the Z axis is determined by the axial direction of the filament; the Y axis is defined consistently. Although technical specifications refer to point sources, the lamp’s position is used to define the reference system.

Fig. 2
Fig. 2

Polar intensity plots provided by the manufacturer and used as data for building the model. The lamp is a Philips Model P21W Inco K: (a) plane XY, (b) plane XZ, (c) plane YZ.

Fig. 3
Fig. 3

Polar intensity plots for three different samples of the P21W lamp at plane XZ. Note that differences among the samples are significant, so smoothing through simple averaging would lead to incorrect results.

Fig. 4
Fig. 4

Polar intensity plots for data on the fourth plane, tilted 45° from the Y axis. The plots are used as experimental data to validate the model. Axis Y 45 is tilted 45° relative to the Y axis.

Fig. 5
Fig. 5

Initial data from the curve-fitting process for the P21W example. Data from the technical specifications for three independent samples were averaged and smoothed for each plane and plotted on a Cartesian system instead of the original polar system. The circles represent data points. The intensity is plotted in normalized units (n.u.): (a) plane XY, (b) plane XZ, (c) plane YZ.

Fig. 6
Fig. 6

Step-by-step fitting process for the data of plane XZ. In all cases a value of θXZ = θ XZ - 90° was used to center the axis of symmetry of the curve. The intensity is given in normalized units (n.u.). (a) Initial data for the curve-fitting process [the data of Fig. 5(b) averaged on both sides of the axis of symmetry]. (b) Curve fitting of the data modified by the assignment of the data for the second peak to the noise level. (c) Curve fitting of the residual left by the subtraction of the initial data from the analytical expression for the first peak. (d) Comparison of the analytical sum of both curve-fitting steps with the initial data. Except for Fig. 6(a), the circles represent data points, and the solid curves represent the fitted functions.

Fig. 7
Fig. 7

Polar representation of the analytical values obtained from the curve fitting of (a) plane XY, (b) plane XZ, (c) plane YZ.

Fig. 8
Fig. 8

(a) Cartesian representation of the transition of the intensity distributions from plane XY (α = 0°) to plane XZ (α = 90°). (b) Three-dimensional intensity distribution shown through tilted polar plots.

Fig. 9
Fig. 9

Comparison of the analytically obtained and the provided values for a plane tilted by 45° from plane XY around the X axis. The two lightface complete circles represent 50% (inner circle) and 100% (outer circle) of the light intensity emission. The boldface closed curve represents the intensity values calculated by use of the proposed model, and the small open circles represent the experimental data points obtained from the technical specifications shown in Fig. 4.

Fig. 10
Fig. 10

Comparison between the simulated CAD photometric distribution (solid curve) and the experimental one (dashed curve) for a Peugeot T1 fog taillight. The source is the modeled P21W. The agreement of the two sets of data is an additional validation of the source model. Validation takes place at a plane located at X = 10 m. For practical purposes all distances are measured in degrees of elevation over the Y axis: (a) z = 0° (corresponding to the Y axis), (b) z = 2.5°, (c) z = 5°, (d) z = 7.5°, (e) z = 10°.

Tables (1)

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Table 1 Values for All Constants Used in Analytical Expressions (3)–(5) Fitted for Planes XY, XZ, and YZa

Equations (5)

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ξ=fYZα-fYZMINfYZMAX-fYZMIN,
fαθα=fXYθαXYξ+fXZ1-ξ,
IθXY=kXYaXY+bXY1+exp-θXY-cXYdXY,
IθXZ=kXZaXZ+bXZ1+θXZ/cXZdxz+eXZ+fXZ exp- 12θXZ-gXZhXZ2,
IθYZ=kYZaYZ+bYZθYZ+cYZθYZ21+bYZθYZ+dYZθYZ2.

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